Apply Bayes Theorem to solve the following problem: Consider a set of patients coming for treatment in a certain clinic. LetA denote the event that a "Patient has heart disease" and B the event that a "Patient is having high blood pressure(BP)."It isknown from experience that 10% of the patients entering the clinic have heart disease and 5% of the patients are having highBP. Also, among those patients diagnosed with heart disease, 7% are having high BP. Given that a patient with high BP, whatis the probability that he will have heart disease

Assume that the chances of a person having a skin disease are 40%. Assuming thatskin creams and drinking enough water reduces the risk of skin disease by 30% andprescription of a certain drug reduces its chance by 20%. At a time, a patient canchoose any one of the two options with equal probabilities. It is given that afterpicking one of the options, the patient selected at random has the skin disease. Findthe probability that the patient picked the option of skin creams and drinking enoughwater using the Bayes theorem.Assume E1: The patient uses skin creams and drinks enough water; E2:The patient uses the drug; A: The selected patient has the skin disease

A national survey reported that 32% of adults in a certain country have hypertension (high blood pressure). A sample of 22 adults is studied. Round the answers to four decimal places.Part 1 of 4(a) What is the probability that exactly 6 of them have hypertension?The probability that exactly 6 of them have hypertension is .Part 2 of 4(b) What is the probability that more than 8 have hypertension?The probability that more than 8 have hypertension is .Part 3 of 4(c) What is the probability that fewer than 3 have hypertension?The probability that fewer than 3 have hypertension is .Part 4 of 4(d) Would it be unusual if more than 10 of them have hypertension?It ▼(Choose one) be unusual if more than 10 of them find have hypertension since the probability is

A version of bayes rule: P(cause|effect) = P(effect|cause)* P(cause)/P(effect)In this example effect = the state of a patient having red dots on the skin cause = the state of a patient having rubellaPrior probabilities: P(cause) = 1/1000, P(effect)= 1/100.P(effect|cause) = 0.9What is the value of P(cause|effect) 0.9 0.09 0.009

c. Student A tells his professor that he forgot to submit his assignment. From pastexperience, the professor knows that students who finish their assignment on timeforget to submit it 1 in 100 times. He also knows that half the students who have notcompleted their assignments will tell him they forgot to submit. He thinks that 90% ofthe students in his class finished their assignments on time.Using Bayes’ theorem defined in Equation (1) and calculate:P(E Hi) ⋅ P(Hi)P(Hi E) =∑kn=1 P(E Hn) ⋅ P(Hn) Equation (1)i. What is the prior probability that a student forgets to submit his/her assignment?Show how P(E) and P(Hi) are defined to calculate this prior probability. (8 marks)ii. What is the probability that student A is telling the truth, i.e. he/she finished theassignment but forgot to submit it? (5 marks)[13 Marks]

A person can have one of the four blood types A, B, AB, and O. The proportions of the four blood types in a given population are(0.2, 0.3, 0.25, 0.25) respectively. Suppose the likelihood of a certain disease X in a person depends on the person's blood type as follows: A: 0.1, B: 0.1, AB: 0.2, and O: 0.4. a) What is the probability of disease X in a person chosen uniformly at random from the population? b) Knowing that the selected person has disease X, what is the probability that their blood type is A?